PCA: Transforming standardized values to non-standardized values

Question:

I have a question related to a PCA. It involves the target or desired value and projected forecast:

  • The PCA gives excellent PC Values, but they are centered around zero since they are standardized.
  • All desired/target values are positive since the markets only have positive values.

Here's what I've done so far: I've modeled and created a forecast for each variable separately using the PC values time series. Next, I computed each input variable's standardized corresponding values Using the loadings (weights) and the PC forecast values. 

I'm trying to figure out how to transform standardized predicted values back to non-standardized forms. Are there specific Excel functions that could help with this process?

Answer:

The process of standardization entails subtracting the mean and then dividing the result by the standard deviation.

$$y_i = \frac{x_i - \bar{x}}{s}$$

To reverse the effect:

$$ x_i = y_i \times s + \bar{x}$$

  1. Compute each series's average ($\bar x$) and the standard deviation ($s$).
  2. Multiply the forecast value (in the standardized form) by the standard deviation (step 1).
  3. Add the average (computed in step 1) to the product (computed in step 2).

The above-outlined calculations should resolve the scaling (de-standardization) issue. You can do this in Excel using the STDEV(.) and AVERAGE(.) functions.

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